Abstract
This research is concerned with the fracture mechanics of a laminated composite medium, which contains a central layer sandwiched by two outer layers. There is a periodic array of cracks in the central layer along the central axis of the medium. Fourier transform is used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the problem, is conducted. Numerical solutions for the crack tip field and the stress in the medium are obtained for various values such as crack length, crack spacing and layer thickness. Results are also given for the reduction of the equivalent Young’s modulus of the laminate due to multiple cracking. The cases of axial extension and residual temperature change of the composite medium are accounted for.
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References
Reifsnider K., Liao K., McCormick R.M.: Fiber fracture in continuous fiber ceramic composites: concepts and observations. J. Eng. Gas Turbines Power Trans. ASME 119, 205–211 (1997)
Park J.M., Kong J.W., Kim J.W., Yoon D.J.: Interfacial evaluation of electrodeposited single carbon fiber/epoxy composites by fiber fracture source location using fragmentation test and acoustic emission. Compos. Sci. Technol. 64, 983–999 (2004)
Landis C.M., McMeeking R.M.: A shear-lag model for a broken fiber embedded in a composite with a ductile matrix. Compos. Sci. Technol. 59, 447–457 (1999)
Wang J., Karihaloo B.L.: Multiple cracking in angle-ply composite laminates. J. Compos. Mater. 29, 1321–1336 (1995)
Camanho P.P., Davil C.G., Pinho S.T.: Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear. Compos. Part A Appl. Sci. Manuf. 37, 165–176 (2006)
Knops M., Bogle C.: Gradual failure in fibre/polymer laminates. Compos. Sci. Technol. 66, 616–625 (2006)
Nguyen B.N., Tucker B.J., Khaleel M.A.: A mechanistic approach to matrix cracking coupled with fiber-matrix debonding in short-fiber composites. J. Eng. Mater. Technol. Trans. ASME 127, 337–350 (2005)
Qu J., Hoiseth K.: Evolution of transverse matrix cracking in cross-ply laminates. Fatigue Fract. Eng. Mater. Struct. 21, 451–464 (1998)
Goyal V.K., Jaunky N.R., Johnson E.R.: Intralaminar and interlaminar progressive failure analyses of composite panels with circular cutouts. Compos. Struct. 64, 91–105 (2004)
Karbhari V.M.: Effects of constituent scale on stress transfer and matrix cracking. Fatigue Fract. Eng. Mater. Struct. 15, 995–1007 (1992)
Hashin Z.: Analysis of stiffness reduction of cracked cross-ply laminates. Eng. Fract. Mech. 25, 771–778 (1986)
McCartney L.N.: Prediction of ply crack formation and failure in laminates. Compos. Sci. Technol. 62, 1619–1631 (2002)
Gudmundson P., Alpman J.: Initiation and growth criteria for transverse matrix cracks in composite laminates. Compos. Sci. Technol. 60, 185–195 (2000)
Adolfsson E., Gudmundson P.: Matrix crack initiation and progression in composite laminates subjected to bending and extension. Int. J. Solids Struct. 36, 3131–3169 (1999)
Gudmundson P., Ostlund S.: Prediction of thermoelastic properties of composite laminates with matrix cracks. Compos. Sci. Technol. 44, 95–105 (1992)
Razvan A., Reifsnider K.L.: Fiber fracture and strength degradation in unidirectional graphite epoxy composite-materials. Theor. Appl. Fract. Mech. 16, 81–89 (1991)
Zhang H., Minnetyan L.: Variational analysis of transverse cracking and local delamination in [0 m /90 n ] s laminates. Int. J. Solids Struct. 43, 7061–7081 (2006)
Kashtalyan M., Soutis C.: Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates. J. Mater. Sci. 41, 6789–6799 (2006)
Diaz A.D., Caron J.F., Ehrlacher A.: Analytical determination of the modes I, II and III energy release rates in a delaminated laminate and validation of a delamination criterion. Compos. Struct. 78, 424–432 (2007)
Choi S., Sankar B.V.: Fracture toughness of transverse cracks in graphite/epoxy laminates at cryogenic conditions. Compos. Part B Eng. 38, 193–200 (2007)
Wang J., Karihaloo B.L.: Mode II and Mode III stress singularities and intensities at a crack tip terminating on a transversely isotropic–orthotropic bimaterial interface. Proc R. Soc. Lond. A 444, 447–460 (1994)
Wang J., Karihaloo B.L.: Mode I stress singularity and intensity at a crack tip terminating on an isotropic-orthotropic bimaterial interface. Int. J. Fract. 74, 325–340 (1996)
Chiu H.P., Yang J.M., Graves J.A.: Effect of fiber coating on creep-behavior of sic fiber-reinforced titanium aluminide matrix composites. J. Mater. Res. 9, 198–206 (1994)
Thayer R.B., Yang J.M.: Creep-behavior of sic fiber-reinforced hot-pressed si3n4 composites. Mater. Sci. Eng. A 160, 169–179 (1993)
Jeng S.M., Yang J.M., Yang C.J.: Fracture mechanisms of fiber-reinforced titanium-alloy matrix composites, III toughening behavior. Mater. Sci. Eng. A 138, 181–190 (1991)
Nied H.F.: Periodic array of cracks in a half plane subjected to arbitrary loading. ASME J. Appl. Mech. 54, 642–648 (1987)
Sih, G.C., Chen, E.P.: Cracks in composite materials. In: Sih, G.H. (ed.) Mechanics of Fracture. Martinus Nijho, The Hague (1981)
Walls D.P., Bao G., Zok F.W.: Mode I fatigue cracking in a fiber reinforced metal matrix composite. Acta Metall. Mater. 41, 2061–2071 (1993)
Bao G., McMeeking R.M.: Thermomechanical fatigue cracking in fiber reinforced metal-matrix composites. J. Mech. Phys. Solids 43, 1433–1460 (1995)
Nairn J.A.: On the calculation of energy release rates for cracked laminates with residual stresses. Int. J. Fract. 139, 267–293 (2006)
Walls D.P., McNulty J.C., Zok F.W.: Multiple matrix cracking in a fiber-reinforced titanium matrix composite under high-cycle fatigue. Metall. Mater. Trans. A 27, 1899–1907 (1996)
Okabe T., Takeda N., Komotori J., Shimizu M., Curtin W.A.: A new fracture mechanics model for multiple matrix cracks of SiC fiber reinforced brittle-matrix composites. Acta Mater. 47, 4299–4309 (1999)
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Wang, B.L., Han, J.C. Transverse cracking of orthotropic composite laminates: a fracture mechanics approach. Arch Appl Mech 80, 1301–1316 (2010). https://doi.org/10.1007/s00419-009-0374-2
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DOI: https://doi.org/10.1007/s00419-009-0374-2